Background: Temporal changes of the proportional abundances of different antibiotics (e.g. mixing or cycling) is regarded as an effective administrative control strategy to reduce the prevalence of antibiotic-resistant pathogens in nosocomial infections. Although such a mixing strategy appears to be plausible, a rigorous assessment of its efficacy is lacking. In particular, a sound mathematical method that correlates temporal changes on both sides, i.e. the consumption of antibiotics and the prevalence of pathogens, is still pending. Methods: We adopt diverse measures of heterogeneity and diversity based on the concept of entropy from other fields and adapt them to the needs in assessing antibiotic resistance. Most important, we extent the measures such that they optimally account for the temporal changes in heterogeneity of antibiotics consumption and pathogen prevalence. Furthermore, we introduce a scheme based on linear regression for the assessment of associations between changes of heterogeneities on the antibiotics and the pathogen side. Results: A crucial part of our results is the derivation and provision of a sound mathematical basis to assess administrative control strategies against antibiotic resistance. As a showcase, we apply the derived methods to records of antibiotics consumption and prevalence of antibiotic-resistant germs from the University Hospital Dresden, Germany. Since the data has not been recorded in a controlled way, the application has to be understood as proof-of-concept. Besides the reasonable quantification of heterogeneities of antibiotics consumption and prevalence of pathogens, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a change of heterogeneity of antibiotics consumption. Conclusions: Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance. Provided that an interventional or comparative study yields different time courses of controlled mixing strategies, the method is potentially suitable to determine optimal counter-strategies by means of statistical learning, aka the maximum entropy method.